This can be easily fixed by assigning the controller to a different player on the control mappings screen. Also, check this out: https://streetsofrogue.tumblr.com/troubleshooting
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Actually, the game doesn't even technically have Steam DRM. You can copy-paste the files from the Steam directory somewhere else if you want to share it that badly. The game will still work, aside from multiplayer.
The primary advantage of Steam is that I update the game frequently. You won't get those updates automatically if you don't use it. Frankly, I think this trumps most intangible freedoms you might have with a completely Steam-free version.
The full version has 5 areas instead of 2, more characters, 4 player couch coop instead of 2, online multiplayer, a "home base" with unlockables, achievements, and a bunch of other stuff. This is effectively more of a demo at this point.
Were you able to run the game before? If it didn't run at any point, I'm not really sure what the issue could be -- probably something with Unity. Searching for Unity problems with your setup would be a good place to start.